A172286 Numbers of circuits of length 2n in K_{n,n} (the complete bipartite graph on 2n vertices).

2, 32, 1458, 131072, 19531250, 4353564672, 1356446145698, 562949953421312, 300189270593998242, 200000000000000000000, 162805498773679522226642, 158993694406781688266883072, 183466660386537233316799232018

Offset: 1

Author

Thibaut Lienart (syncthib(AT)gmail.com), Jan 30 2010

Keywords

• easy
• nonn

Comments

Circuits are allowed to be self-intersecting and are directional with a designated start node. The number of (self-avoiding) directed cycles is given by A010790. - Andrew Howroyd, Sep 05 2018

Examples

			a(2) = 32 because there are 32 circuits of length 4 in the complete bipartite graph K2,2.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A010790, A118537.

Programs

MATLAB

nmax = 10;
for k=1:nmax
an = 2*k^(2*k);
fprintf('%3.0f ', an);
end

PARI

a(n)=2*n^(2*n); \\ Andrew Howroyd, Sep 05 2018

Formula

a(n) = 2*n^(2*n).

Extensions

More terms from Max Alekseyev, Jan 18 2012